Meshless inverse method to determine temperature and heat flux at boundaries for 2D steady-state heat conduction problems

• An inverse method to predict boundary temperature and heat flux is proposed.
• Accuracy depends on number, position and error of temperature measurements.
• Additional heat flux measurement significantly improves the prediction accuracy.
• Heat flux and temperature measurement positions should be aligned with each other.

Inverse determination of temperature and heat flux at an inaccessible surface of a solid has been widely employed in recent years. In this paper, a meshless inverse method, i.e. the method of fundamental solution (MFS), has been developed to determine the temperature field and hence the local boundary temperature and heat flux distributions for a 2D steady-state heat conduction problem based on temperature measurements at interior sample points in the wall of the boundary. A case study showed that MFS predicts the boundary temperature and heat flux with about the same accuracy as the Beck’s function specified method but consumes significantly less computing time. Error analysis was carried out regarding uncertainty in location and accuracy of temperature measurement to demonstrate the reliability of the proposed method.